Parliament has until Aug, 15 to approve the charter and submit it to a national referendum in mid-October under a formula strongly supported by the Americans. But major differences remain among the ethnic and religious groups represented on the committee.
"I will suggest to the committee drafting the constitution now to postpone the period for a maximum of 30 days," Hammoudi told The Associated Press as he went into a closed-door committee meeting.
Hammoudi's comment came after framers of the new constitution said they expected to submit a draft in time for parliament to meet the deadline for approval, though they added decisions on some key points may be deferred until a later date.
The United States has been pushing the Iraqis to meet the deadline to maintain political momentum seen as crucial to defeating the insurgency and enabling U.S. and other foreign troops to begin leaving Iraq next year.
Main points in dispute include such issues as federalism, dual nationality and the role of Islam.
A Sunni member of the committee, Saleh al-Mutlaq, suggested postponing a decision the most troublesome issues until after the Dec. 15 general elections.
The constitution should be approved by parliament by Aug. 15 and submitted to the voters in a referendum two months later.
In other developments:
The bomb targeted a police vehicle as it was passing on a main road near the town of Haswa, 30 miles south of Baghdad, said police Capt. Muthanna Khaled Ali. One police vehicle was damaged in the attack, he said.
The United States hopes that a new Iraqi constitution will help calm the insurgency by encouraging the country's disaffected Sunni Arab community to abandon the conflict and join the political process.
But the violence continued Saturday, with the two Britons, who worked for the security firm Control Risks Group, killed when a roadside bomb exploded alongside a British consulate convoy in Basra, Iraq's second-largest city, 340 miles southeast of Baghdad.
Elaayan said that his bodyguard was injured in the attack, which took place near an Iraqi army checkpoint.
"I was surprised that the soldiers did not react or come to help us although the checkpoint was less than 100 meters from where the attack took place," he said.
Sunni leaders have accused the Shiite-led government of sanctioning attacks by Shiite military forces against the Sunni community.
Two weeks ago, a member of the National Dialogue Council who was participating in the constitutional committee was assassinated in Baghdad, along with another Sunni committee adviser and a bodyguard. Mijbil Issa's death prompted a week-long walkout by his Sunni colleagues, who only returned to the committee process after getting assurances for additional security.
The U.S. leadership has placed high hopes on a constitution that will lay the foundation for a broad-based government. There is an Aug. 15 deadline for the charter to be approved by the National Assembly, and it will then move to a public referendum in October.
Adnan al-Dulaimi was dismissed July 24 as head of the Sunni Endowment, the government agency in charge of the upkeep of Sunni mosques and shrines, Prime Minister Ibrahim al-Jaafari's office said Saturday.
Al-Dulaimi told The Associated Press he was fired for defending Sunnis, who dominated Iraqi politics under Saddam Hussein but feel marginalized by the current U.S.-backed, Shiite-dominated government. Drawing Sunnis into the political process is seen as key for legitimizing any Iraqi government.
"I think that the reason behind my dismissal is that they want to silence a voice that is speaking against unjustified practices against Sunnis such as arrests, torture in the prisons, and also for my calls to release innocent detainees and to save Iraq from sectarianism, insecurity and divisions," al-Dulaimi said.
Al-Dulaimi had been among a handful of Sunni Muslim clerics and officials who have urged fellow Sunnis to vote in the constitutional referendum slated for October and the general elections that will follow in December. Most Sunnis boycotted the Jan. 30 balloting.
Tension between the Sunni Muslim minority and the Shiite community has been on the rise, with recent reports of Sunnis being detained and killed by Shiite-led military forces.
Dozens of bodies--blindfolded, bound and shot--have been discovered around Baghdad and central Iraq, many of them Sunnis. Earlier this month, 11 Sunni detainees died in police custody after suffocating inside a locked van in the midday heat. A criminal investigation into the deaths is underway.
On Friday, about 1,000 Sunnis staged a protest near the heavily guarded Green Zone, accusing the Shiite-dominated government's security forces of killing Sunnis under the guise of fighting terrorism.
Most members of the minority Sunni Arab community, which forms the core of the anti-American insurgency, stayed home during the country's landmark Jan. 30 elections, either fearing insurgent attacks or heeding boycott calls by rebels and hard-line clerics.
That helped Shiites and Kurds win control of the new government, since only 17 Sunni members made it into the 275-member parliament.